Asymptotic Accelerated Expansion in String Theory and the Swampland

We study whether the universal runaway behaviour of stringy scalar potentialstowards infinite field distance limits can produce an accelerated expandingcosmology \`{a} la quintessence. We identify a loophole to some proposed boundsthat forbid such asymptotic (at parametric control) accelerated expansion in 4d$\mathcal{N}=1$ supergravities, by considering several terms of the potentialcompeting asymptotically. We then analyse concrete string theory examplescoming from F-theory flux compactifications on Calabi-Yau fourfolds, extendingprevious results by going beyond weak string coupling to different infinitedistance limits in the complex structure moduli space. We find some potentialcandidates to yield asymptotic accelerated expansion with a flux potentialsatisfying $\gamma=\frac{\|\nabla V\|}{V}<\sqrt{2}$ along its gradient flow.However, whether this truly describes an accelerated expanding cosmologyremains as an open question until full moduli stabilization including theKahler moduli is studied. Finally, we also reformulate the condition forforbidding asymptotic accelerated expansion as a convex hull de Sitterconjecture which resembles a convex hull scalar WGC for the membranesgenerating the flux potential. This provides a pictorial way to quicklydetermine the asymptotic gradient flow trajectory in multi-moduli setups andthe value of $\gamma$ along it.